Stochastic contagion models without immunity: their long term behaviour and the optimal level of treatment

In this paper we analyze two stochastic versions of one of the simplest classes of contagion models, namely so-called SIS models. Several formulations of such models, based on stochastic differential equations, have been recently discussed in literature, mainly with a focus on the existence and uniqueness of stationary distributions. With applicability in view, the present paper uses the Fokker–Planck equations related to SIS stochastic differential equations, not only in order to derive basic facts, but also to derive explicit expressions for stationary densities and further characteristics related to the asymptotic behaviour. Two types of models are analyzed here: The first one is a version of the SIS model with external parameter noise and saturated incidence. The second one is based on the Kramers–Moyal approximation of the simple SIS Markov chain model, which leads to a model with scaled additive noise. In both cases we analyze the asymptotic behaviour, which leads to limiting stationary distributions in the first case and limiting quasistationary distributions in the second case. Finally, we use the derived properties for analyzing the decision problem of choosing the cost-optimal level of treatment intensity.

     

Theoretical study on the mechanism and kinetics of addition of hydroxyl radicals to fluorobenzene

Geometries, frequencies, reaction barriers, and reaction rates were calculated for the addition of OH radical to fluorobenzene using Möller–Plesset second‐order perturbation (MP2) and G3 methods. Four stationary points were found along each reaction path: reactants, prereaction complex, transition state, and product. A potential for association of OH radical and fluorobenzene into prereaction complex was calculated, and the associated transition state was determined for the first time. G3 calculations give higher reaction barriers than MP2, but also a significantly deeper prereaction complex minimum. The rate constants, calculated with Rice–Ramsperger–Kassel–Marcus (RRKM) theory using G3 energies, are much faster and in much better agreement with the experiment than those calculated with MP2 method, as the deeper well favors the formation of prereaction complex and also increases the final relative populations of adducts. The discrepancies between the experimental and calculated rate constants are attributed to the errors in calculated frequencies as well as to the overestimated G3 reaction barriers and underestimated prereaction complex well depth. It was possible to rectify those errors and to reproduce the experimental reaction rates in the temperature range 230–310 K by treating the relative translation of OH radical and fluorobenzene as a two‐dimensional particle‐in‐the‐box approximation and by downshifting the prereaction complex well and reaction barriers by 0.7 kcal mol^?1. The isomeric distribution of fluorohydroxycyclohexadienyl radicals is calculated from the reaction rates to be 30.9% ortho, 22.6% meta, 38.4% para, and 8.3% ipso. These results are in agreement with experiment that also shows dominance of ortho and para channels. © 2012 Wiley Periodicals, Inc.     

Development of inductively coupled plasma atomic emission spectrometry for palladium and rhodium determination in platinum-based alloy

Inductively coupled plasma atomic emission spectroscopy (ICP-AES) with internal standardization was applied for the analysis of an in-house reference platinum alloy containing palladium and rhodium (approximately 5% by weight). In order to compensate for variations in signal recovery due to matrix interferences, and therefore to improve the precision, platinum, the major component, was chosen as an internal standard. Quantitative analysis was based on calibration using a set of matrix-matched calibration standards with and without employing the internal standard. These results were compared with those obtained by X-ray fluorescence (XRF) spectroscopy. The results for both techniques were in a good agreement, although the precision was slightly better in the ICP-AES technique, with or without the internal standard.     

Phenolic compounds in field horsetail (Equisetum arvense L.) as natural antioxidants

In this paper, the study of antioxidant activity and phenolic composition of three different extracts (EtOAc, n-BuOH and H(2)O) of field horsetail (Equisetum arvense L.) is presented. The antioxidant activity has been evaluated measuring the total reducing power (expressed by Ascorbate Equivalent Antioxidant Capacity - AEAC), inhibition of lipid peroxidation, and free radical scavenging capacity (RSC) towards 2,2-diphenyl-1-picrylhydrazyl (DPPH radical) and nitric oxide (NO), respectively. In addition, the total flavonoid content (TFC) and phenolic constituents of each extract have been determined. The results obtained show that the highest RSC regarding both DPPH and NO radicals is expressed by EtOAc extract (EC(50)=2.37 microg/mL and EC(50)=90.07 microg/mL, respectively), and the lowest by H(2)O extract (EC(50)=37.2 microg/mL and EC(50)>333.33 microg/mL, respectively). n-BuOH extract showed the highest total reducing power (AEAC=13.40 microg/mL). Differences in the phenolic composition of examined extracts are found comparing the HPLC chemical profiles. Although, isoquercitrin is the main flavonoid in both EtOAc and n-BuOH extracts, a considerable amount of di-E-caffeoyl-meso-tartaric acid was presented in the n-BuOH extract. In H(2)O extract high content of phenolic acids and low percentage of flavonoids were detected.     

Superelectrophilic amidine dications: dealkylation by triflate anion

Superelectrophiles: Formamides were designed that when treated with triflic anhydride would be transformed into superelectrophilic amidine dications. These dications were so electrophilic that they underwent in?situ dealkylation by the triflate anion (see scheme; Tf=trifluoromethanesulfonyl). DFT calculations were used to determine the mechanistic details of the dealkylation reaction.     

Estimation of Rayleigh scattering loss in a double-clad photonic crystal fiber

In this paper the effect of photonic crystal fiber’s structure parameters on Rayleigh scattering was investigated. Rayleigh scattering loss (RSL) has been numerically estimated by average Rayleigh scattering coefficient based on the empirical relations for \(V\) and \(W\) parameters of double-clad photonic crystal fibers (DC PCFs). The dependence of RSL on the two structural parameters—the air hole diameter and the hole pitch was demonstrated. We have shown that RSL depends on the index profiles because of the different optical power confinement factors in every layer of DC PCF. Using these results, the RSL can be optimized by adjusting the fiber parameters—air-hole diameter as well as the air-hole pitch.     

Thermal Diffusion Process Estimation for Fabrication of Graded Plastic Optical Fibre

Thermal diffusion of dopants is investigated in the process of generating the graded-index profile of plastic optical fibres. Because the diffusion coefficient in high polymers has been shown to depend strongly on dopant concentration, it is allowed in this work to vary with the radial coordinate of the multistep-core fibre. A novel multi-layer model is presented for solving the diffusion equation with the variable diffusion coefficient. It is solved by the finite difference method. The solution determines the dopant diffusion profile in the fibre. It is verified against a solution from the literature and two cases of fibres with diffused profiles. The application is demonstrated on two examples of graded-index plastic optical fibres, one originally with a two-step and the other with four-step core. The results indicate that closer to the core-cladding interface, the computed diffused profile with variable diffusion coefficient D is closer to target profile than the profile obtained with constant D for the same time of thermal process.